This document provides the definition and an example of using the quotient rule to differentiate a fraction. The quotient rule is defined as the derivative of the denominator times the numerator minus the numerator times the derivative of the denominator, all over the denominator squared. As an example, the derivative of (3x+4)/(x-4) is calculated using the quotient rule and simplifies to (24x-13)/(x-4)^2.

1. BUSINESS
MATHEMATICS
DIFFERENTIATION(QUOTIENT RULE)

2. QUOTIENT RULE
DEFINITION:
The quotient rule is defined as the quantity of
the denominator times the derivative of the
numerator minus the numerator times the
derivative of the denominator all over the
denominator squared.
 
 
       
  
.2
xg
xfxgxgxf
xg
xf
dx
d 







3. EXAMPLE
SOLUTION
Differentiate.
Let and . Then, using the quotient rule
x
xx 34 24

  34 24
 xxxf   xxg 
     
2
2424
24 3434
34
x
x
dx
d
xxxx
dx
d
x
x
xx
dx
d






 
   
2
243
13484
x
xxxxx 

2
24
343
x
xx 

Now simplify.

4. Thank
you